We converted the continuous integral representation (REF ) into discretized forms as a summation over all the particles in the support domain. This process is also commonly known as particle approximation in the SPH literature [1]}. Writing the particle approximation as follows
\(<f(\mathbf {r})>=\sum _{j=1}^{N}\dfrac{m_j}{\rho _j}f(\mathbf {r_j})W(|\mathbf {r}-\mathbf {r_j}|,h),\) 
